# Homework Help: Thermodynamics, ideal gas, virial coefficient

1. Jul 12, 2013

### scorleon0511

1. The problem statement, all variables and given/known data
So the problem gives you the compressibility factor Z. It gives two equations, one for ideal gas and other one for non-ideal gas.
The question states:
The second Virial coefficient B(T) depends on the temperature T and is related to the intermolecular potential B(T) = 2[itex]\pi\N∫[1-exp(-ψ(r)/kT)]r^2 dr

boundary is 0 ~ ∞.

Derive the second Virial coefficient B(T) when the dependence of the intermolecular potential ψ(r) on molecular distance r is given as follows,

r < σ : ψ(r) = ∞,
r >= σ : ψ(r) = -ε(σ/r)^6

2. Relevant equations
Z = 1 + (n/V)*B(T) + (n/V)^2 * C(T) + (n/V)^3 * D(T)+...
for ideal gas, it is : Z = PV / nRT.
B(T), C(T), and D(T) are the second, the third, and the fourth virial coefficients respectively. P is a pressure, V is a volume, n is the number of moles, R is the gas constant, and T is a temperature. It also gives me a equation with Boltzmann constant k and Avogadro's number N: R = kN.

3. The attempt at a solution
Since the problem have given us different ψ(r) when the boundary of r is different, I decided to separate the integral into two parts also, one with boundary of 0~σ and the second one with σ~∞. From there I decided to substitute the ψ(r) into corresponding integrals, one ∞ into the one with boundaries of 0~σ and -ε(σ/r)^6 into the one with σ~∞. I thought I can derive from this but I seem to get stuck when I'm deriving the integral with the boundary of σ~∞. Please give me some help me with some advice!